Giải phương trình sin 3 x = cos 5x .

\(\begin{array}{l}\sin 3x = \cos 5x \Leftrightarrow \cos \left( {\frac{\pi }{2} - 3x} \right) = \cos 5x\\{\rm{                      }} \Leftrightarrow \left[ \begin{array}{l}\frac{\pi }{2} - 3x = 5x + k2\pi \\\frac{\pi }{2} - 3x =  - 5x + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{{16}} + k\frac{\pi }{4}\\x =  - \frac{\pi }{4} + k\pi \end{array} \right.\,\,(k \in \mathbb{Z})\end{array}\)